Dr Moeller has worked in Horsham, Victoria for two years, leading the intensive care of patients and supervising other GPs in the region of about 54,000 residents.
He says he will fight to stay in Australia.
He says the family, including his son, is happy in Horsham.
"He loves this town and he has his mates and taking part of community life and he can contribute," he said.
"I don't think he's a burden."
Dr Moeller says the Department refused his application on the grounds that Lukas's disability would be a significant and ongoing cost to the Australian community.
"It's essentially saying we don't want you here to live here permanently because you have a disabled son and because you are a burden to the Australian community," he said.
"That's not nice however you put it. And it's nothing personal, I know that, I think it's a real shame to treat people like that."
Victorian Premier John Brumby has written a letter requesting a review of the doctor's treatment.
"It's gone off to the Federal Minister, I've asked for this review to be undertaken as a matter of urgency," he said.
Brumby says the Department has made a "stupid" decision.
"I think a serious error has occurred in the way in which this case has been assessed," he said
"We're very, very concerned about this and obviously, in my view, a serious error has been made by the federal authorities."
"This is a case we would want to see reversed and overturned at the earliest possible opportunity."
Australia's Federal Human Rights and Disability Discrimination Commissioner, Graeme Innis, says the Immigration Department's decision is disappointing.
"These decisions are made only taking the negatives into account," he said.
"In other words there is a cost assessed to support a young person with a disability.
"What's not taken into account is the major positive contributions those of us in Australia with disabilities have made to society."
Federal Health Minister Nicola Roxon plans to take the matter up with Immigration Minister Chris Evans.
"We know how valuable and important it is to have doctors in our rural and regional community and I'm sure that that will also be taken into account," she said.
Immigration Department spokesman Peter Vardas says an objective process will decide whether Dr Moeller can continue to practice in Horsham.
Vardas says he understands the community's outrage, but a clear review process is in place.
"Certainly there's a lot of community support for Dr Moeller, as there has been in cases in years gone by," he said.
"At the end of the day it is an objective process. The Migration Review Tribunal, when it gets to them, will review the circumstances and they may uphold the Department's decision, they may overturn the Department's decision.
Horsham residents have started a petition supporting the doctor.